Fundamentals in ECD – Maths
Learner's Manual
Writers:
Fundamentals in ECD : Mathematical Literacy
Learner’s Manual
Fundamentals in ECD:
Mathematical Literacy
Learner’s Manual
Writers
Penny Smith (COUNT), Victoria Lindsay, Aarnout Brombacher, Penny Hansen, Sheila Drew
Editor
Ian Moll (SAIDE)
South African Institute for Distance Education
Fundamentals in ECD : Mathematical Literacy
Learner’s Manual
Published by: South African Institute for Distance Education (SAIDE)
PO Box 31822
Braamfontein
2017
South Africa
Tel: + 27 11 403 2813
Fax: + 27 11 403 2814
Email: [email protected]
Website: http://www.saide.org.za
Fundamentals in ECD
Communications Level One Learner’s Manual
ISBN: 0-620-360-48-8
© South African Institute for Distance Education (SAIDE)
First Published 2006
Creative Commons License
The copyright for this work is held by the South African Institute for Distance Education (SAIDE). However, to
maximise distribution and application, the work is licensed under the Creative Commons License. This allows
you to copy, distribute, and display the work under the following conditions:
By attribution. You must give the original authors credit, and acknowledge the role of the Zenex
Education Foundation in sponsoring the work, in the terms that appear below.
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who charge a fee for access to the work, or for training programmes that make use of the work, are not
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No derivative works. You may not alter, transform, or build upon this work.
Share alike. For any reuse or distribution, you must make clear to others the license terms of this
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Any of these conditions can be waived if you get permission from SAIDE.
Editor: Ian Moll (SAIDE)
Writers: Penny Smith (COUNT), Victoria Lindsay, Aarnout Brombacher, Penny Hansen, Sheila Drew
Critical Reader: Erna Lampen
Illustrations: Andre Plant
Design and Layout: Design Intervention
The development of this manual has been sponsored by the Zenex Education Foundation. However, the opinions
that it expresses are those of the contributing authors, and not necessarily those of the Foundation.
ii
ACKNOWLEDGEMENTS
These materials comprise both original text and sources from other published materials
that have been used and adapted where necessary with permission form the materials
developers or publishers.
COUNT wishes to acknowledge the following sources:
Heinemann Publishers for permission to adapt selected activities from their
OUTCOMES MATHS series (no longer in print)
Malati Public Domain Materials (funded by the Open Society Foundaiton)
Ukuqonda Public Domain Materials produced for the Delta Foundation
The South African Institute of Race Relations for the use of graphs from the
2004-5 SAIRR Survey.
For artwork from Franco Frescura, Rural Shelter, (RAVAN PRESS) drawing of a
beehive hut in Module 3, Activity 1.
Problem Centred Mathematics for the use and adaptation of the following selected
activities:
Module 1
Unit 6: Activity 7
Unit 8: Activity 5-10
Module 2
Unit 8: Activity 2
Module 3
Unit 6: Activities 2-3
Unit 7: Activities 2-7
Unit 10: Activities 1-3
Unit 11: Activity 9
iii
Fundamentals in ECD : Mathematical Literacy
iv
Learner’s Manual
Contents
CONTENTS
Introduction
vi
1. Who is this manual for?
vi
2. ECD Fundamentals
vi
3. Unit Standard Outcomes
vii
4. Language of learning
vii
5. The learning cycle
viii
6. How to use your Manual
ix
7. What you need
x
8. Assessment
xi
9. Using your journal for the first time
xi
10. Bantwana bami
xiii
Fundamentals Communication Unit Standards
xiv
1. Unit Standard 7451
xiv
2. Unit Standard 7449
xv
3. Unit Standard 7463
xvi
4. Unit Standard 7453
xvii
5. Unit Standard 7461
xviii
6. Unit Standard 7450
xviii
7. Unit Standard 7448
xiv
8. Unit Standard 7447
xx
9. Unit Standard 7464
xxii
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Fundamentals in ECD : Mathematical Literacy
Learner’s Manual
INTRODUCTION
1.
Who is this manual for?
This manual is for you, the ECD practitioner. You will use it to study for
Fundamentals in Mathematical literacy at NQF Level One. It is written so that
you can work through it alone, or with other early childhood practitioners in a
small study group, or in a workshop group with a trainer. Read the introduction
carefully alone or with your study group or trainer, to make sure you understand
what you are doing. As you work through the activities you will slowly address
all the Unit Standard Outcomes for Fundamentals in Mathematical literacy.
2.
ECD Fundamentals
Fundamentals in Mathematical Literacy form one part of a full ECD qualification
at Level One. For a full qualification you need to have 120 credits. These are made
up like this:
ECD Core: 48 credits
ECD Elective: 36 credits
Fundamentals Communication: 20 credits
Fundamentals Mathematical Literacy: 16 credits
You can see that for Fundamentals Mathematical Literacy you need to get 16
credits. That means that you should spend about 160 hours, or 20 days, studying
on this course. This time includes study outside of workshops such as on
assignments and portfolio work. Remember that some people will need more
time, and others will not need as much.
vi
Introduction
3.
Unit Standard Outcomes
There are eight Unit Standards for Fundamentals Mathematical literacy. They
show what you need to be able to do (the specific outcomes) and how well you
must be able to do them (the Assessment Criteria). These are the unit standards
covered by this Manual:
ID
Fundamentals
Mathematical
literacy
Additional Unit
Standard not
specified for
ECD Level One
Qualification
Unit Standard Title
Level
Credits
7451
Collect, analyse, use and communicate
numerical data
Level 1
2
7449
Critically analyse how mathematics is used
in social, political and economic relations
Level 1
2
7463
Describe and represent objects and the
environment in terms of shape, space, time
and motion
Level 1
2
7453
Use algebraic notation, conventions and
terminology to solve problems
Level 1
3
7461
Use maps to access and communicate
information concerning routes, location and
direction
Level 1
1
7450
Work with measurement in a variety of contexts
Level 1
2
7448
Work with patterns in various contexts
Level 1
4
7464
Analyze cultural products as representations of
shape, space and time
Level 1
2
7447
Work with numbers in various contexts
Level 1
6
Credits needed for Mathematical literacy (16)
The last Unit Standard number 7447 is not required for a Level One ECD
Qualification, but we have addressed it in this course because we think it is very
helpful and relevant to your work with children.
We have included some sections which are not specified in the Unit Standards, for
example the theorem on Pythagoras. We have included them because the Unit
Standards are currently being reviewed, and we believe these sections may be
included in the new Unit Standards.
There is a list of all the Unit Standard Specific Outcomes and Assessment Criteria
on page xiv.
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Fundamentals in ECD : Mathematical Literacy
4.
Learner’s Manual
Language of learning
This manual is written in English. Maybe English is your second, or even third
language. You may need help with some of the English in this manual. You might
need a dictionary, or perhaps you know someone who can translate some of the
difficult language for you.
We have created a dictionary in the margin on each page. Add new words to the
dictionary whenever you want to. Maybe studying will be easier if you are in a
group learning together with one Trainer. You can have discussions in home
languages and ask for translations anytime. But we are assuming that you will be
assessed in English.
5.
The learning cycle
In this manual you will see there are new ideas for you to read and think about.
There are activities for you to do and there are opportunities for you to think
about what you have learned. Think of this as a learning cycle or learning path.
It does not really matter where you begin in the cycle. You may begin with a new
idea, do an activity, and then go back to the new idea before you think about what
you have learned. You could also begin with an activity, look at new information
and then think about what you have learned. Good learning will always include
all three parts of the cycle. The learning cycle can be drawn like this:
New Ideas /
New Content
Activity
viii
What have
you learned?
Introduction
DICTIONARY:
icon – small picture
6.
How to use your Manual
Structure
All the way through the manual you will see the same cycle that you saw above.
Each part of the cycle has an icon to show what it is:
Activity
In each activity you will do something, think about what you have done, and
discuss or write down your thoughts. You can do most of the activities in your
Manual unless you need more space. Sometimes the Manual will show that you
have to do an activity on a separate paper for your portfolio. There is a time
shown for each activity. This is only a guide because different learners may need
different amounts of time. It does not really matter how much time you spend, as
long as you find it meaningful, and you are sure that you understand.
New ideas/content
Often there are some new ideas for you to read and think about before you do an
activity. This might be information that you know already, or it might be new
information. These ideas will also prepare you for the activity.
What have you learned?
After activities there is writing that will help you to think about what you have
learned.
There are other parts in the manual too. They also have icons. These are:
Calculator
There will be times when you need to use a calculator. This little icon will show
you when it is appropriate to use a calculator. There are other times when you
might want to use a calculator but it is better to do the calculations without the
help of a calculator.
Linking your learning to your ECD work
We want you to think about what you will teach children from what you have
learned in this course. This section in ach unit will help you to think about that.
We believe that it is not good teaching practice to force ideas onto children. So do
not go and simply teach them what you have learned. What you have learned is
at the wrong level for young children. There will be times when children show
interest in something related to what you have learned. You can link the
children’s interest to something you have learned here and work at the right level
with children.
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Fundamentals in ECD : Mathematical Literacy
Learner’s Manual
Portfolio Work
This icon shows when it will be good for you to put activities or assignments into
your portfolio for assessment.
Self-assessment Checklist
You can use the self-assessment checklist to check your progress against the listed
outcomes. They will also help your Trainer to keep track of how you are progressing.
Using a Journal
A journal is a book where you can reflect on your experience as a learner and as
a teacher. There may be times when you feel worried about something. Then you
can write down your worries. You can write down tips and reminders to yourself.
Next to this icon you will always see a set of questions which will help you to
think about what to write. Answer these questions in your own words in your
journal. Remember to put a date every time you write in your journal.
DICTIONARY:
reflect on – think about
The purpose of your journal is:
• To make your ideas clearer to yourself by writing them down
• To express your feelings about your learning
• To keep track of your progress in your learning. This is another kind of selfassessment. You will keep a record of your understanding throughout the
course. You can come back to something you have written in your journal and
see how your understanding has changed.
• To practice writing without worrying about handwriting, grammar, spelling,
correct order, paragraphs and other things. This will be very good for your
writing skills, believe it or not.
7.
What you need
• A punched exam pad for your exercises and assignments. You will file these
assignments in your portfolio
• A file to keep your work safe and in order. File your work as you go along –
don’t leave it to the last minute. This file will be your portfolio.
• A pen or pencil
• A dictionary. Some good dictionaries for this level are:
SA Oxford Dictionary for Adult Learners
Pocket Oxford Dictionary
SA Schools Dictionary
Mini Dictionaries
You can buy these at any big branch of JUTA or CNA.
• An exercise book to use as your journal
• A calculator
You may need other resources for some activities. These will be listed for you.
x
Introduction
8.
Assessment
Your trainer will provide you with a clear assessment guide. You must check that
your trainer has arranged for you to be assessed by an accredited fundamentals
agency, like IEB or UNISA. If you are studying on your own or in a study group
make sure you register with an assessment agency to be assessed. These are the
only organisations that can assess you and give you credits for your qualification.
When you are assessed you will be assessed against the Unit Standard outcomes.
Some of the activities can be used for assessment. These activities and all the
assignments will go into your portfolio. You will see the Portfolio Work icon next
to these activities and assignments. In addition to your portfolio you will do an
exam (test).
Your Trainer will only do formative assessment to help you prepare for the final
assessment. Formative assessment is not assessment for credit.
What is a portfolio?
A portfolio is a collection of your work that you show to a qualified assessor. Of
course, it should all be your own work, not copied. If your work is satisfactory,
the portfolio will help to prove that you are competent in NQF1 Mathematical
literacy. In this course your portfolio will contain:
• Some activities
• All your assignments
• Your journal
9.
Using your journal for the first time
Remember the purpose of your journal is:
• To make your ideas clearer to yourself by writing them down
• To express your feelings about your learning
• To keep track of your progress in your learning.
In the next set of activities you will begin to write your journal. Do the activities
in your journal.
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Fundamentals in ECD : Mathematical Literacy
Learner’s Manual
Activity 1:
Using your journal to learn
Write all these answers in your journal.
Time needed
55 minutes
1. Explain in writing what a journal is. Write in your home language. Use your
own words - don’t just translate directly from the explanation in this manual.
2. Explain verbally what a journal is. Speak to somebody who speaks a language
other than English.
3. Write down in your home language how you feel about writing a journal. Ask
yourself these questions:
a. Have I done journal writing before?
b. Am I still a bit worried about writing a journal?
c. Is writing in my journal harder than I thought or easier?
d. Do I usually worry about punctuation and spelling and grammar every
time I write?
e. Did I manage to forget about grammar etc while I was writing in my
journal?
4. Complete this sentence in English in your journal:
For me, writing in my journal ………..
Congratulations! You have just completed your first entry in your journal.
Now do Activity 2.
Activity 2:
Writing a journal to suit the purpose
Time needed
40 minutes
Work alone
1. Look at the first writing activity in your journal and answer the following
questions in writing in your journal:
a. How will you know when you wrote in your journal?
b. How will you know what activity you were writing about?
c. Did you write full sentences? Are full sentences helpful?
d. Would it help if you highlighted or underlined ideas, wrote them in colour,
added arrows and numbers?
e. Do you think you could draw some pictures in your journal?
f. Discuss your answers with someone who is also using a journal.
Remember your journal is not only to write down answers to questions, it is also
a place for you to write down your feelings. Your feelings about your learning are
not right or wrong. It may take a little time to get used to writing your real
feelings. But often it is the best way to learn.
xii
Introduction
Linking using a journal with your ECD work
This is the first time in the course that you are going to think about how your
learning links with your work as an ECD practitioner. These questions might help
you to think about it some more:
a. Can children keep a journal?
b. How can children keep a journal if they cannot write? Are there other ways
of recording thoughts and feelings?
c. What kind of things do you think children can draw or write about?
d. What do you think children can learn from keeping a journal?
e. How do you think you can help children to understand what a journal is?
f. How can you help children to write down their thoughts and feelings?
g. Why is it useful for children to think about their feelings?
There will be more opportunities for you to discuss these ideas later on in the
manual. For now we want you to know that we think it is important for young
children to learn to reflect on their thoughts and feelings.
10. Bantwana Bami
Finally, let us introduce you to some of the characters you will meet in this
manual.
Mrs Refiloe Maseko is the teacher and principal at Bantwana Bami home-based
day care centre. She has 18 children in her care and she uses her garage, a room
in her house and her yard to provide a space for the children to play and work.
Mrs Maseko does the very best for her children. She makes sure she spends time
chatting with them, reading to them, asking them questions and listening to them.
Mrs Dlamini is a friend of Mrs Maseko. She runs an ECD centre in the next
village. They often sit together and chat about their work.
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Fundamentals in ECD : Mathematical Literacy
Learner’s Manual
Fundamentals Mathemactical Literacy
Unit Standards
1.
Unit Standard 7451
Collect, analyze, use and communicate numerical data
Specific Outcomes and Assessment Criteria:
SO1:
Identify situations for investigation and data collection and collect numerical
data.
1. Situations for data collection are identified in terms of the purpose for data
collection.
2. Appropriate methods are selected to collect data.
3. A variety of appropriate data collection methods are used to collect data from
primary and secondary sources. (Surveys, books, interviews, observations,
tally sheets and questionnaires.)
4. The potential misuse of data achieved through the data collection method is
described.
5. Reasons for and limitations of using sampling are described.
SO2:
Classify and analyze numerical data. (Grouped and ungrouped data.)
1. Data is organized for meaningful analysis. (Classification, ordering, listing.)
2. Analytical tools are used correctly and appropriately to analyze the data.
(Median, mean, modes, frequency, range.
3. The differences between and uses of mean, median and mode are described.
SO3:
Summarize and display organized numerical data. (Graphs: pie, frequency
polygon, histogram, simple bar graph, stem and leaf. Tables, basic tree diagrams.)
1. The form of display is appropriate to the data and context, and is justified in
terms of its appropriateness.
2. The scale is selected and used for a reasonable presentation of the data, and the
scale is justified in terms of its reasonableness.
3. Different forms of display are identified and evaluated in terms of their
purposes.
SO4:
Extract, interpret and critically evaluate information from various forms of
display. (Graphs: pie, frequency polygon, histogram, simple bar graph, stem and
leaf. Tables, basic tree diagrams.)
1. The information extracted from the display is consistent with the display.
2. The information is interpreted to form informed opinions.
3. Displays that distort information are identified and the manner in which they
distort information is described.
4. The effect of distortions in displays is described in terms of the impact on
meaning in social, socio-historical, political and economic contexts.
xiv
Introduction
5. Projections or predictions are made in a manner that is consistent with the
display.
6. The information is analyzed to determine and report on the validity of data
collection methods, forms of display and projections that are made.
7. Communication of findings is clear, consistent with the display and makes use
of accepted terminology.
SO5:
Demonstrate understanding of the concept of chance and calculate simple
probabilities. (Limited to systematic counting strategies.)
1. Situations are identified in which chance arises.
2. Simple probabilities are determined.
3. Statements of chance are correctly interpreted.
4. The number of combinations and the probability of a particular event are
determined.
5. Probabilities are used to address simple real or simulated problems.
2.
Unit Standard 7449
Critically analyze how mathematics is used in social, political and economic
relations
Specific Outcomes and Assessment Criteria:
SO1:
Critically analyze the use of mathematical language and relationships in the
workplace. (Wage negotiations, salary increases, and productivity as a ratio.)
1. The ways in which mathematics is used in the workplace are described.
(Percentage, graphs, differences, ratio and proportion.)
2. Ways in which mathematical relationships and language can be used to
represent particular perspectives are described. (Different forms of
comparisons such as differences versus ratio. Manipulation of graphs through
choice of graph, scale of axes and nature of axes. Use of different averages:
mean, median, mode. More than one perspective is to be described.)
SO2:
Critically analyze the use of mathematical language and relationships in the
economy. (Budgeting, banks: interest rates, mortgage, service charges; fuel prices;
pensions; inflation; value of the rand and exchange rates.)
1. The ways in which mathematics is used is described. (%, graphs, differences,
ratio and proportion.)
2. Ways in which mathematical relationships and language can be used to
represent particular perspectives are described. (Different forms of
comparisons such as differences versus ratio. Manipulation of graphs through
choice of graph, scale of axes and nature of axes. Use of different averages:
mean, median, and mode. More than one perspective to be described.)
3. The impact of economic changes on the individual is described.
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Fundamentals in ECD : Mathematical Literacy
Learner’s Manual
SO3:
Critically analyze the use of mathematics in social relations. (Social
differentiation: gender, social mobility, race; historical and possible future
contexts, e.g. employment equity; apartheid policies.)
1. Ways in which mathematics can be used as a filter for social differentiation are
described. (Social differentiation includes examples such as entrance
qualifications; number of women doing mathematics.)
2. The significance attached to number by different societies is described.
(Spiritual; superstitious; aesthetic; political.)
3. The use of mathematics in the media is described. (Adverts, reports, sports.)
SO4:
Critically analyze use of mathematics & mathematical language & relationships
in political relations (Income distribution; census; elections; voting; opinion
polls.)
1. The ways in which mathematics is used is described. (Percentage, graphs,
differences, ratio and proportion.)
2. Ways in which mathematical relationships and language can be used to
represent particular perspectives are described. (Different forms of
comparisons such as differences versus ratio. Manipulation of graphs through
choice of graph, scale of axes and nature of axes. Use of different averages:
mean, median, and mode. More than one perspective to be described.)
3. The impact of the use of mathematics in these contexts on individuals and
social groups is described.
3.
Unit Standard 7463
Describe and represent objects and the environment in terms of shape, space, time
and motion
Specific Outcomes and Assessment Criteria:
SO1:
Describe and represent the position and change in position of an object in space.
(Words, rough sketches and abstract representation on a Cartesian plane.)
1. The positions of objects are described in relation to each other using graphs
and sketches and written or verbal descriptions.
2. The positions of objects are represented correctly on a Cartesian plane.
3. The change of position of objects in terms of the relationship between space
and time is described.
4. Tessellations are identified.
xvi
Introduction
SO2:
Illustrate changes in size & shape of appearance of objects as result of changes in
orientation.
1. The perception of the changes in an object is described from different
observational points. (3-dimensional objects and 2-dimensional
representations of 3-dimensional objects.)
2. 3-dimensional objects are represented in 2 dimensions in such a way that the
size and shape of the object are correctly represented.
3. The relationships between surface area and volume are described.
4.
Unit Standard 7453
Use algebraic notation, conventions and terminology to solve problems
Specific Outcomes and Assessment Criteria:
SO1:
Form and use algebraic equations and inequalities to represent and solve
problems. (Simple linear equations and inequalities.)
1. The problem is represented completely through equations or inequalities,
which are consistent with the problem.
2. The concepts of equations and inequalities are explained.
3. Situations requiring the use of equations as opposed to inequalities, and vice
versa, are identified.
4. Algebraic rotation, conventions and terminology are used correctly.
5. The solution is correct in terms of the problem context.
6. The solution is verified through substitution or other verification processes.
SO2:
Manipulate algebraic expressions to find equivalent forms. (Common factors,
products and grouping using associative, distributive and commutative
properties.)
1. The manipulated form is equivalent to the original form. (The original
expression is manipulated to achieve at least two different forms.)
SO3:
Select and use algebraic formulae to solve problems. (Substitution into any
formula, solve for one variable, supplied formulae from any context.)
1. The correct formula is selected in terms of the problem context.
2. The formula is applied correctly to obtain a valid solution.
3. Units are used correctly.
xvii
Fundamentals in ECD : Mathematical Literacy
5.
Learner’s Manual
Unit Standard 7461
Use maps to access and communicate information concerning routes, location
and direction
Specific Outcomes and Assessment Criteria:
SO1:
Read, interpret and use maps, to depict and make sense of real locations,
distances and position (Street maps: local and national maps.)
1. Objects are identified on a map.
2. The positions of objects on a map are given using reference points on a grid.
3. A variety of routes between two points on a map are identified and described.
4. Appropriate routes are identified and selected to meet the requirements of a
variety of circumstances.
5. Real distances between points on a map are determined correctly in
accordance with the scale.
6. Landmarks are used to give direction in real life, and these landmarks are
identified and located on a map.
7. Directions are given correctly using maps and in real life. (Bearing and the four
compass points.)
SO2:
Draw maps according to scale. (Non-contoured maps.)
1. Maps are drawn such that the relative positions of places and objects match
the real situation.
2. A suitable scale is chosen, indicated and applied correctly.
3. Symbols used conform to conventional uses or are defined through a key or
legend.
4. The map is clear and neat and contains all critical information as required by
the situation.
5. Maps are converted from one scale to another.
6.
Unit Standard 7450
Work with measurement in a variety of contexts
Specific Outcomes and Assessment Criteria:
SO1:
Apply relationships between common quantities in various contexts. (Mass and
weight, distance and displacement, speed and velocity, volume and density,
volume and surface area, area and perimeter, distance and time, volume and
capacity.)
1. Terms are used in the proper context.
2. Comparisons between quantities are made and differences and relationships
described.
3. Formulae and units are described in context to show the relationships and
differences.
xviii
Introduction
SO2:
Use measuring instruments to measure and calculate quantities in various
contexts. (Quantities include all of: length, distance, mass, time, temperature,
volumes of regular prisms, perimeter, area, weight, surface area, density,
displacement and angles. Measuring instruments include all of: rulers, tape
measures, scale, clocks, thermometers, capacity measuring instruments, and
protractors.)
1. Measuring instruments are used correctly.
2. Readings are recorded and reported within the margin of error as limited by
the instrument and as is appropriate within the context.
3. Measuring instruments are chosen to comply with the accuracy requirements
of the context.
SO3:
Solve measurement problems in various contexts. (Practical and non-practical
processes, trigonometric right-angled heights and distances.)
1. Solutions are correct within margins of error allowed within the context.
2. Units are used correctly.
3. Methods and solutions are justified.
7.
Unit Standard 7448
Work with patterns in various contexts
Specific Outcomes and Assessment Criteria:
SO1:
Recognize, identify and describe patterns in various contexts. (Numeric,
geometric, patterns from a variety of contexts.)
1. Patterns are recognized in terms of the relationship between the elements of
the pattern.
2. Patterns are correctly identified in terms of the relationship between the
elements of the pattern.
3. Patterns are correctly described in terms of the relationship between the
elements of the pattern and remain consistent through the pattern.
4. The language of comparison is appropriate and describes the relationship
between the elements of the pattern.
SO2:
Complete, extend and generate patterns in a variety of contexts. (Numeric,
geometric, patterns from a variety of contexts.)
1. Completed patterns are internally consistent with respect to the relationship
between elements of the pattern.
2. The extension is consistent with respect to the relationship between elements
of the pattern.
3. Generated patterns are internally consistent.
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Fundamentals in ECD : Mathematical Literacy
Learner’s Manual
SO3:
Devise processes for a general rule. (Processes include: systematic counting,
sequencing numbers, tables, drawings, pictures, classification, organized lists,
mathematical and models such as graphs.)
1. Appropriate processes are devised according to the context.
2. Processes have potential to lead to a general rule.
3. A general rule is devised such that it is consistent with the relationship of the
elements of the patterns.
SO4:
Represent patterns using different generalized mathematical forms. (Graphs,
formulae, expressions and other rules for expressing patterns.)
1. Appropriate mathematical forms are used to represent patterns.
2. The representation is consistent with relationships within the pattern and
represents the pattern completely.
3. Conversions are made between various forms of representations.
4. Relationships between various possible forms of representations are
described.
SO5:
Use general rules to generate patterns. (Processes include: systematic counting,
sequencing numbers, tables, drawings, pictures, classification, organized lists,
mathematical models such as graphs.)
1. Patterns generated are consistent with the general rule.
2. Patterns are generated to the extent that they enable the rule to be devised
from the pattern.
8.
Unit Standard 7447
Working with numbers in various contexts
Specific Outcomes and Assessment Criteria:
SO1:
Express and interpret a range of contexts using mathematical symbols and find
applications for numerical models. (Everyday problems, numerical contexts.
Numerical models include equations, expressions and terms.)
1. Mathematical sentences reflect the situation completely and accurately.
(Everyday problems, numerical contexts. Numerical models include
equations, expressions and terms.)
2. The form of expression is appropriate to the context.
3. Application for given numerical models are developed such that the meaning
of symbols and relationships between them are clarified.
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Introduction
SO2:
Solve a range of everyday problems using estimation and calculations. (Rounding
off and truncating, with or without calculator, combination, separation,
comparison, equalisation, sharing and grouping.)
1. Problem solving strategies are based on a correct interpretation of the problem
situation.
2. Estimates can be justified within context.
3. Calculations are performed accurately.
4. Calculations follow some form of logical reasoning process, which is
presented clearly.
5. Solutions are correct in terms of the context.
SO3:
Verify and justify solutions within different contexts. (Solutions derived by
learners and by others.)
1. The reasoning process is explained clearly.
2. Solutions are justified in terms of the context. (Appropriate and inappropriate
solutions.)
3. Solutions are shown to be consistent with estimations and vice versa.
SO4:
Perform operations on simple and complex numerical expressions. (Four basic
operations in all combinations. Expressions involving exponents that can be
calculated without a calculator. Operations to be performed with and without a
calculator.)
1. Operations are performed according to the conventions governing the order of
operations.
2. Solutions are correct.
SO5:
Describe and compare counting systems from different cultures. (Own, African
culture other than own, one other.)
1. Numbers are translated from one base system to another. (Base 2, 5, 10, and
16.)
2. Descriptions show understanding of how counting systems developed and
their significance.
3. Descriptions show examples of how the systems might have been used, and
the limitations of the system.
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Fundamentals in ECD : Mathematical Literacy
Learner’s Manual
SO6:
Critically analyze the development of the base ten number system. (Place value,
role of 0 in our number system, patterned nature of whole numbers, history and
contestations.)
1. The development and significance of zero is explained.
2. Understanding of the place value of numbers is demonstrated. (Expansion of
numbers in different ways, the value of a numerical symbol in a number.)
3. The patterned nature of whole numbers and its historical development are
described.
4. The contestations around, and use and popularisation of the decimal number
system are described. (Uses in economics and politics.)
SO7:
Analyze the relationship between rational and whole numbers.
1. Demonstrations describe the increasing density of the system.
2. Demonstrations show that whole numbers are a subset of rational numbers.
3. The properties of whole numbers and rational numbers are given.
SO8:
Analyze the relationship between rational numbers and integers.
1. Demonstrations describe the increasing density of the system.
2. Demonstrations show that whole numbers are a subset of rational numbers.
3. The properties of whole numbers and rational numbers are given.
9.
Unit Standard 7464
SO1
Identify geometric shapes and patterns in cultural products. (shapes of and
decorations on cultural products such as drums, pots, mats, buildings, and
necklaces.)
1. Basic transformations are identified. (translations, reflections and rotations.)
2. Basic geometric shapes are identified.
3. Basic patterns are identified and described.
4. Basic patterns are extended in a way that maintains the consistency of the
pattern.
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Introduction
SO2
Analyze similarities & differences in shapes & patterns, & effect of colour, used by
cultures. (analyze similarities and differences in shapes and patterns, and the
effect of colour, used by different cultures.)
1. Similarities in shapes and patterns are identified.
2. Differences in shapes and patterns are identified.
3. Possible reasons for similarities and/or differences in shapes and patterns
used by different cultures are identified.
4. The effect of colour on shape and symmetry is described and illustrated.
SO3
Analyze and explain the way shapes and space are used in different epochs and
cultures. (Architecture, town and settlement planning.)
1. Shapes used by different cultures are identified.
2. The use of space in different cultures is analyzed and explained.
3. The use of space in different epochs is analyzed.
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